nowadays, it is common to find optimal point of the dynamic problem; dynamic problems whose optimal point changes over time require algorithms which dynamically adapt the search space instability. in the most of them, the exploitation of some information from the past allows to quickly adapt after an environmental change (some optimal points change). this is the idea underlining the use of memo...

The construction of local reduced-order models via multiscale basis functions has been an area of active research. In this paper, we propose online multiscale basis functions which are constructed using the offline space and the current residual. Online multiscale basis functions are constructed adaptively in some selected regions based on our error indicators. We derive an error estimator whic...

Solving large Partially Observable Markov Decision Processes (POMDPs) is a complex task which is often intractable. A lot of effort has been made to develop approximate offline algorithms to solve ever larger POMDPs. However, even stateof-the-art approaches fail to solve large POMDPs in reasonable time. Recent developments in online POMDP search suggest that combining offline computations with ...

The coupling of a free flow with a flow through porous media has many potential applications in several fields related with computational science and engineering, such as blood flows, environmental problems or food technologies. We present a reduced basis method for such coupled problems. The reduced basis method is a model order reduction method applied in the context of parametrized systems. ...

We propose an improvement to the reduced basis method for parametric partial differential equations. An assumption of affine parameterization leads to an efficient offline-online decomposition when the problem is solved for many different parametric configurations. We consider an advection-diffusion problem, where the diffusive term is nonaffinely parameterized and treated with a two-level affi...

Reduced basis (RB) methods are effective methods for model reduction of parametrized partial differential equations (P2DEs). During the last years various types of stationary and timedependent, linear and nonlinear P2DEs have been treated. In the field of dynamical systems’ order reduction, these methods are largely unknown, but the interest in reduction of parametrized systems is increasing. I...

Planning in partially observable environments remains a challenging problem, despite significant recent advances in offline approximation techniques. A few online methods have also been proposed recently, and proven to be remarkably scalable, but without the theoretical guarantees of their offline counterparts. Thus it seems natural to try to unify offline and online techniques, preserving the ...

We propose a data-driven stochastic method (DSM) to study stochastic partial differential equations (SPDEs) in the multiquery setting. An essential ingredient of the proposed method is to construct a data-driven stochastic basis under which the stochastic solutions to the SPDEs enjoy a compact representation for a broad range of forcing functions and/or boundary conditions. Our method consists ...